Exercise 43 Page 82

To solve the given equation, let's factor and solve using the Zero Product Property. At the end, we will check that our answer is correct.

Factoring

To begin, let's rewrite the equation with all the non-zero terms on the left-hand side. After that, we will proceed to factoring.

Solving

Now we can apply the Zero Product Property to solve.

x(x-3)=0

ZeroProdProp

Use the Zero Product Property

lcx=0 & (I) x-3=0 & (II)

AddEqn

(II): LHS+3=RHS+3

lx_1=0 x_2=3

The solutions for our equation are 0 and 3.

Checking

To check our answers, we will substitute them for x in the given equation. Let's start with x=0.

x^2=3x

Substitute

x= 0

0^2? =3( 0)

CalcPow

Calculate power

0? =3(0)

ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that x=0 is a solution of the equation. Let's now check x=3.

x^2=3x

Substitute

x= 3

3^2? =3( 3)

CalcPow

Calculate power

9? =3(3)

Multiply

Multiply

9=9 ✓

This is also a true statement, so we know that x=3 is a solution of the equation.